As shown in Japanese Patent Application Laid-open (JP-A) Nos. 2004-293395 And 2002-147291, an exhaust cooling unit for an engine is known where a double-pipe structure has an inner pipe and an outer pipe in which an exhaust control valve is arranged at the upstream side in the interior thereof. An exhaust cooler is arranged between the inner and outer pipes and this performs heat exchange between a coolant water and exhaust gas.